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计算流体力学(CFD)方法不仅仅起到数值模拟的作用,它本身是一个复杂的非线性系统。在流动稳定性分析、气动弹性分析、优化设计以及流动控制等领域,从系统的角度出发,对CFD数学模型线性化后,可以对模型的系统矩阵进行定量分析获得更多的系统特性。但是CFD数学模型往往非常复杂且阶数很高,因此其线性化系统矩阵的获得比较困难。鉴于此,采用人工编程和自动微分相结合,构造有限体积法并行CFD模型的线性化系统矩阵。其中自动微分只被用来得到每个界面通量的局部雅可比矩阵,而采用人工编程方法来实现并行环境下的稀疏雅可比矩阵的组装。线性化系统的并行求解采用了块雅可比预处理的广义最小残量法,每个并行进程内部则采用零填充不完全LU分解预处理。为了验证这种线性化方法,上述方法被用于:1NACA 0012翼型的非定常绕流线性系统构造与求解;2NACA 0012翼型稳态流动的伴随方程构造与求解;3AGARD wing 445.6机翼颤振问题降阶建模。上述三个算例的结果与CFD模拟的吻合一致。
Computational fluid dynamics (CFD) method not only plays the role of numerical simulation, it is itself a complex nonlinear system. In the field of flow stability analysis, aeroelastic analysis, optimization design and flow control, the system matrix of the model can be quantitatively analyzed to obtain more system characteristics from the system point of view after linearizing the CFD mathematical model. However, the mathematical models of CFD are often very complex and orderly, so the linearized system matrix is more difficult to obtain. In view of this, a linearized system matrix of finite volume method parallel CFD model is constructed by combining artificial programming and automatic differentiation. Automatic differentiation is only used to get the local Jacobian matrix of each interface flux, but the artificial programming method is used to realize the assembly of sparse Jacobian matrix in parallel environment. The linear system parallel solution uses the block Jacobian preprocessing generalized minimum residual method, each parallel process internal zero fill incomplete LU decomposition preprocessing. In order to validate this linearization method, the above method is used to construct and solve the unsteady flow around 1NACA 0012 airfoil; to construct and solve the 2NACA 0012 airfoil steady-state flow accompanying equation; 3AGARD wing 445.6 wing flutter Problem reduction modeling. The results of the above three examples are consistent with the CFD simulation.